# Differences

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partial_monoids [2018/07/23 17:42]
jipsen created
partial_monoids [2018/07/23 17:43] (current)
jipsen
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====Definition==== ====Definition====
-A \emph{partial monoid} is a structure $\mathbf{A}=\langle A,\cdot,e\rangle$, where $\langle A,\cdot,e\rangle$ is a [[partial semigroup]] and+A \emph{partial monoid} is a structure $\mathbf{A}=\langle A,\cdot,e\rangle$, where $\langle A,\cdot\rangle$ is a [[partial semigroup]] and
$e$ is an identity for $\cdot$: $x\cdot e=x=e\cdot x$ for all $x\in A$. $e$ is an identity for $\cdot$: $x\cdot e=x=e\cdot x$ for all $x\in A$.